| Deriving bit-serial circuits in Ruby (1991) | |||||||||||||||
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| The action of bit-serial arithmetic circuits is often explained in purely pictorial terms. In contrast, this paper describes an attempt to deal with the systematic development of bit-serial arithmetic circuits within a mathematical framework which we have previously used to develop parallel circuits. A well-known bit-serial adder is formally shown to implement the specification of an adder, without any recourse to detailed arguments about snapshots or specific arguments about sequences of inputs. 1 DESIGN BY CALCULATION Ruby [1] is a language of relations and functions that supports a style of development by calculation. A circuit is represented by a relation between the signals at its terminals, and forms of circuit are captured by functions which operate on those relations. For example, if the second terminal of a two-terminal component R is connected to the first of a similar component S, they behave as R ; S, defined by x (R ; S) y , 9z. x R z & z S y. At another extreme, the pa... | |||||||||||||||
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